**Subject :**Electrical Machines II (AC Machines)

**Unit :**Synchronous motor

## Construction of V-curves

**Construction of V-curves:**

- The V-curves of a synchronous motor show how armature current varies with its field current when motor input is kept constant. These are obtained by plotting a.c. armature current against d.c. field current while motor input is kept constant and are so called because of their shape (Fig. 1).

- There is a family of such curves, each corresponding to a definite power intake. In order to draw these curves experimentally, the motor is run from constant voltage and constant-frequency bus-bars.

- Power input to motor is kept constant at a definite value. Next, field current is increased in small steps and corresponding armature currents are noted. When plotted, we get a V-curve for a particular constant motor input.

- Similar curves can be drawn by keeping motor input constant at different values. A family of such curves is shown in Fig. 1.

Detailed procedure for graphic construction of V-curves is given below:

1. First, constant-power lines are drawn.

2. Then, with A as the centre, concentric circles of different radii AB, AB1, AB2, etc. are drawn where AB, AB1, AB2, etc., are the back e.m.fs corresponding to different excitations. The intersections of these circles with lines of constant power give positions of the working points for specific loads and excitations (hence back e.m.fs). The vectors OB, OB_{1}, OB_{2} etc., represent different values of ER (and hence currents) for different excitations. Back e.m.f. vectors AB, AB_{1} etc., have not been drawn purposely in order to avoid confusion (Fig. 2).

3. The different values of back e.m.fs like AB, AB_{1}, AB_{2}, etc., are projected on the magnetization and corresponding values of the field (or exciting) amperes are read from it.

4. The field amperes are plotted against the corresponding armature currents, giving us ‘V’ curves.